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C₉×D₁₈₅₃ #45688662

order	33354
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₁₈₅₃
unambiguous semidirect product	C₁₇⋊(C₉×D₁₀₉)

Splittings

Fitting, Hall	C₉×C₁₇×C₁₀₉ ⋊ C₂
derived, Hall	C₁₇×C₁₀₉ ⋊ C₂×C₉
Hall	C₉×C₁₀₉ ⋊ D₁₇
Hall	C₉×C₁₇ ⋊ D₁₀₉
Sylow	C₁₀₉ ⋊ C₉×D₁₇
Sylow	C₁₇ ⋊ C₉×D₁₀₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₁₈₅₃
commutator, hypocenter	C₁₇×C₁₀₉	C₂×C₉
Frattini	C₃	C₃×D₁₈₅₃
Fitting	C₉×C₁₇×C₁₀₉	C₂
socle, cosocle	C₃×C₁₇×C₁₀₉	C₂×C₃
prime radical	C₃×D₁₈₅₃	C₃
LCS	G ▷ C₁₇×C₁₀₉
UCS	C₁ ◁ C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 16677

Conjugacy classes & character table

8352 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33354, 5);